{"title":"格上覆盖半径问题的硬度","authors":"I. Haviv, O. Regev","doi":"10.1109/CCC.2006.23","DOIUrl":null,"url":null,"abstract":"We provide the first hardness result for the covering radius problem on lattices (CRP). Namely, we show that for any large enough p les infin there exists a constant cp > 1 such that CRP in the lscrp norm is Pi2-hard to approximate to within any constant less than cp. In particular, for the case p = infin, we obtain the constant Cinfin = 1.5. This gets close to the constant 2 beyond which the problem is not believed to be Pi2-hard. As part of our proof, we establish a stronger hardness of approximation result for the forallexist-3-SAT problem with bounded occurrences. This hardness result might be useful elsewhere","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"23 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"27","resultStr":"{\"title\":\"Hardness of the covering radius problem on lattices\",\"authors\":\"I. Haviv, O. Regev\",\"doi\":\"10.1109/CCC.2006.23\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We provide the first hardness result for the covering radius problem on lattices (CRP). Namely, we show that for any large enough p les infin there exists a constant cp > 1 such that CRP in the lscrp norm is Pi2-hard to approximate to within any constant less than cp. In particular, for the case p = infin, we obtain the constant Cinfin = 1.5. This gets close to the constant 2 beyond which the problem is not believed to be Pi2-hard. As part of our proof, we establish a stronger hardness of approximation result for the forallexist-3-SAT problem with bounded occurrences. This hardness result might be useful elsewhere\",\"PeriodicalId\":325664,\"journal\":{\"name\":\"21st Annual IEEE Conference on Computational Complexity (CCC'06)\",\"volume\":\"23 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2006-07-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"27\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"21st Annual IEEE Conference on Computational Complexity (CCC'06)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/CCC.2006.23\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2006.23","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Hardness of the covering radius problem on lattices
We provide the first hardness result for the covering radius problem on lattices (CRP). Namely, we show that for any large enough p les infin there exists a constant cp > 1 such that CRP in the lscrp norm is Pi2-hard to approximate to within any constant less than cp. In particular, for the case p = infin, we obtain the constant Cinfin = 1.5. This gets close to the constant 2 beyond which the problem is not believed to be Pi2-hard. As part of our proof, we establish a stronger hardness of approximation result for the forallexist-3-SAT problem with bounded occurrences. This hardness result might be useful elsewhere
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